Converting GPS coordinates to X, Y, Z coordinates

Question

So here is the basic problem. I am currently working on a GPS system in C# in Unity 3D (the person that has given us the assignment is making us use this program, so I can't do it in anything else).

Now I've run in to a small problem, basically we are able to request (what we think are decimal) coordinates from an android phone, but now we are trying to convert those coordinates to X, Y, Z coordinates. Preferebly X and Z, because we do not actually need height. However everything we have been finding on the internet so far has been for a conversion to a sphere map where as we just have a basic flat digital map.

If anyone knows how to convert the coordinates we have to the basic X and Z coordinates (so our longitude and latitude) it'd be amazing.

To quickly note I am not sure if the sort of coordinates we have are actual decimal coordinates so this is what they look like:

Latitude: 53.228888 Longitude: 6.5403559

these coordinates should end up on "Wegalaan 3, Groningen, The Netherlands" if you would look them up on a map.

Thanks already!

EDIT: (this is also in the comments)

Sorry if it might be confusing. Honestly I only half understand how all this works, anyways to clear some things up. I am currently working in Unity with a simple 2D map I got from the internet of the city I live in (Groningen, The Netherlands) and I am trying to basically take GPS coordinates I get from my android phone and then show them on that map with a red dot, however to do this I need to be able to move the red dot to the right coordinates on the map. What I am trying to do is convert the GPS coords (lon and lat) to X and Z (Unity3D flat coordinates, may also just be X and Y) so that if I align the map right I get a small GPS system for just my city. If you are curious as to why I am doing this it is simply because a friend of mine and me are trying to build a game using our city and this GPS system as a basis

EDIT2:

except that I'll be honest I have no idea how cartesian coordinates work, but they seem to be what I am looking for yes :P Coordinates on a flat plane and with X,Y coords I mean basically just coordinates I could use in Unity3D on a flat 2D plane which is what I am working in.

EDIT3:

Thanks for the answers, to start. This is not a duplicate, secondly my friend and I already found the stackoverflow topic you sent me, but it seems to not be working for us (maybe we did something wrong). Basically the north and south distance between different places we tested with that formula have worked, however the east west distance between them was way bigger than it should have been. We think it might be because that formula was meant for a spherical earth, but maybe we did something wrong. If someone could explain further that'd be amazing!

EDIT4:

We are sure it can't be our map that is wrong in any way, because we have aligned it with multiple locations. We got the coordinates for these locations and then used this website: http://www.gpscoordinaten.nl/converteer-rd-coordinaten.php to convert it to XY coordinates and then used these XY coordinates to check if our map would align properly. It did, so we are sure there is some problem with the maths we are using and not with our actual map.

EDIT5: Removed many, many grammatical errors. It's way too hot over here to be writing properly right now, so I am very very sorry if any of this makes no sense. just let me know and I'll edit to try and explain what we are trying to do.

EDIT6: Found my own asnwer, it is down in between all the other answers if you wanna see what I did to fix my problem

Answer 1

By now I have found the answer to my own question (actually found it a little while ago already, but totally forgot to post it here)

Basically I made a little formula of my own that multiplied the coordinates with a set number (depending on wether or not it is the x or y axis) that is the difference between two set coordinate points. These two points are the outer points of my map.

Basically by doing this I can get quite accurate measurements I haven't even had a meter difference to my actual position yet.

I know this sounds a bit vague and I don't entirely know how to explain it, but for anyone interested here is the code I use:

void RetrieveGPSData()
{
    currentGPSPosition = Input.location.lastData;
    System.DateTime dateTime = new System.DateTime(1970, 1, 1, 0, 0, 0, 0);
    dateTime = dateTime.AddSeconds(currentGPSPosition.timestamp);

    float z = latToZ (Input.location.lastData.latitude);
    float x = lonToX (Input.location.lastData.longitude);

    this.transform.position = new Vector3 (x, 0f, z);

    gpsString = ("Last Location: " + Input.location.lastData.latitude.ToString () + " " + Input.location.lastData.longitude.ToString () + " " + Input.location.lastData.altitude.ToString () + " " + Input.location.lastData.horizontalAccuracy.ToString () + " " + dateTime.ToShortDateString() +" "+ dateTime.ToShortTimeString());
}

float latToZ (double lat){

    lat = (lat - 53.178469) / 0.00001 * 0.12179047095976932582726898256213;
    double z = lat;

    return (float)z;
}

float lonToX (double lon){

    lon = (lon - 6.503091) / 0.000001 * 0.00728553580298947812081345114627;
    double x = lon;

    return (float)x;
}

Now for anyone wondering why I took the 53.something and the 6.something off the lon and lat it is because the coordinate of my 0 X and 0 Z point in Unity which corresponds to the bottom left corner of my map, which is one of the two points I talked about that I use for this calculation.

I hope this helps anyone else who might ever be stuck on something similar and if you have any questions feel free to ask them.

-LAKster

Answer 2

Does the map have mercator projection? Is it a world map? If so, the top of the map is usually around latitude 85, latitude 0 at the center vertically. longitude 0 is at greenwich (usually center horizontally), 180/-180 is at the antimeridian/date line, at the left and right edges of the map.

When the latitude is -180, x would be 0, when it's 180, x == width of map.

This link should tell you what you need